Method for controlling a cluster of gyroscopic actuators for producing angular momentum

Abstract

Described is a method for controlling a cluster of gyroscopic actuators of a satellite, the cluster being divided into two coplanar subsets, the method comprising: - receiving a setpoint angular momentum; - determining an angular momentum to be provided by each coplanar subset (Formula I) on the basis of a distribution parameter for distributing, between the two subsets, a component of the setpoint angular momentum along an axis (Formula II) common to both planes, r being a scalar between the lowest allowable value and the highest allowable value of the contribution of one of the coplanar subsets to the component of the setpoint angular momentum along the axis common to both planes; - determining an inclination angle value of each gyroscopic actuator of a subset, on the basis of the angular momentum to be provided by the subset; and - issuing a command for each gyroscopic actuator comprising the respective determined inclination angle value.

Description

Description Title: Method for controlling a cluster of gyroscopic actuators to generate angular momentum technical field

[0001] This disclosure relates to a method of controlling a set of gyroscopic actuators to cause these actuators to produce a set angular momentum. Previous technique

[0002] A gyroscopic actuator 10, also called a gyrodyne, or in English CMG for "Control Moment Gyro," is schematically represented in Figure 1 and comprises a flywheel 11 which is driven in rotation, around an axis of rotation x, by a motor (not shown) at a high constant rotational speed, and an orientation device 12 for the orientation of the flywheel's axis of rotation x in a plane. In Figure 1, the orientation device 12 for the flywheel's axis of rotation x is adapted to drive the axis of rotation x in rotation with respect to an orthogonal axis z. The rotation of the flywheel around its axis of rotation x creates a constant angular momentum that is a function of the rotational speed of the flywheel 11 and its moment of inertia about the axis of rotation.When a speed is applied to the orientation of the rotation axis x of the flywheel, a gyroscopic torque results from the transfer of angular momentum between the CMG and its support.

[0003] It is known, for example from the publication by Michel Llibre, "Gyroscopic Actuators for Attitude Control of Satellites," February 16, 2009, to use gyroscopic actuators for the attitude control of a satellite. In this case, the tilt axis of the flywheel is linked to the satellite frame, so that the rotation axis of the flywheel is mobile relative to the satellite frame, and the gyroscopic torque generated by the gyroscopic actuator is transmitted to the satellite frame and allows the rotation speed of the satellite to be controlled by the principle of conservation of angular momentum of the system comprising the satellite and the gyroscopic actuator(s).

[0004] One disadvantage of using gyroscopic actuators to achieve attitude control concerns singularities, which are configurations of gyroscopic actuators in which there is a direction such that, regardless of the angular velocity of the tilt angle commanded to the gyroscopic actuators, the gyroscopic torque produced is always orthogonal to the direction considered, so that for this configuration it is not possible to achieve control of the gyroscopic actuators allowing instantaneous control of the rotation speed of the satellite.

[0005] The use of gyroscopic actuators for the attitude control of a satellite therefore implies reducing singular configurations as much as possible, in order to increase the operational capabilities of this attitude control solution.

[0006] Furthermore, some control laws used to regulate the tilt angle of gyroscopic actuators, in order to produce a setpoint angular momentum, are not deterministic, in that they do not allow a specific configuration of gyroscopic actuator tilt angles to be associated with a setpoint angular momentum. This can result in the need to stop an ongoing mission in order to desaturate the gyroscopic actuators and return them to their initial configuration, which impacts the successful execution of the mission and entails additional costs for satellite operation. Summary

[0007] This disclosure improves the situation.

[0008] In particular, one purpose of this disclosure is to propose a method for controlling a set of gyroscopic actuators on a satellite, which will increase the operational capabilities of a satellite during a mission.

[0009] Another purpose of this disclosure is to propose a method in which the control of gyroscopic actuators, for a given setpoint angular momentum, is deterministic.

[0010] Another purpose of this disclosure is to propose a satellite attitude control that is applicable with a variable number of gyroscopic actuators.

[0011] Another purpose of this disclosure is to allow the angular momentum capability range of all gyroscopic actuators to be adapted according to mission requirements.

[0012] In this regard, a method is proposed for controlling a set of gyroscopic actuators of a satellite, for the realization by the gyroscopic actuators of a setpoint angular momentum, each gyroscopic actuator comprising a flywheel capable of being driven in rotation around an axis of rotation so as to produce an angular momentum, and a device for orienting the axis of rotation according to an angle o, the gyroscopic actuators being distributed into two coplanar subsets, each coplanar subset comprising at least two gyroscopic actuators configured to generate a respective angular momentum contained in the same plane of the subset, the respective planes of the two subsets being non-coplanar, the ordering process including: the reception of a dimensionless setpoint angular momentum to be generated by all gyroscopic actuators, the determination of an angular momentum to be provided by each coplanar subset, from the dimensionless setpoint angular momentum and a distribution parameter chosen according to a predetermined sequence of distribution parameters, between the two coplanar subsets, of a component of the setpoint angular momentum along an axis common to the two planes, in which the parameter r is a scalar between a value minimum and a maximum value corresponding respectively to the lowest permissible value and the highest permissible value of the contribution of one of the coplanar subsets to the component of the setpoint angular momentum along the axis common to the two planes, the determination of a tilt angle value for each gyroscopic actuator of a coplanar subassembly, based on the angular momentum to be provided by said coplanar subassembly, and the emission of a command from each gyroscopic actuator including the respective determined tilt angle value.

[0013] In some embodiments, the distribution parameter has at least one predetermined value depending on the satellite's mission.

[0014] In some embodiments, the predetermined distribution parameter exhibits a value profile that varies over time during a satellite mission.

[0015] In some embodiments, the parameter r is defined as follows: + T X P XZ = x — X P XY where x PxY and x p xz are respectively the angular momenta generated, along the common axis ( ff ) to the two planes, by the two coplanar subsets, x^ nis the lowest permissible value of the contribution of a subset to said component of the setpoint angular momentum along the common axis ( s ) to both planes, x^ x is the highest permissible value of the subset's contribution to the (x) component of the setpoint angular momentum along the axis ( ff common to both plans.

[0016] In embodiments, it is defined as COS CT, H; [0, 2n[ N D c B 3 sin ct, Eq.2 ct —> A = (x; y; z) ieP XY sin ct, and we define x^ 7711X71 and xl^illM r as = max I - IN y 2 - y 2 ; x - JN z 2 - z 2 x P li x L a ULJC = min ( i -| N y 2 — y J 2 ; ' x + N z 2 - z 2

[0017] In some embodiments, determining an angle value for each gyroscopic actuator of a coplanar subset from the angular momentum to be provided by said subset includes: the determination of a direction of angular momentum to be provided by each gyroscopic actuator, based on the angular momentum to be provided by the sub-assembly, and at least one predetermined parameter, defining an angular separation between the angular momentum to be provided by a reference gyroscopic actuator and the angular momentum to be provided by the sub-assembly, and the determination of a tilt angle value for each gyroscopic actuator from the corresponding angular momentum direction.

[0018] In embodiments, wherein the step of determining a direction of angular momentum to be generated by each gyroscopic actuator comprises: the determination of the direction of the angular momentum of a reference gyroscopic actuator from a first angular separation parameter and the direction of the angular momentum to be provided by the subassembly, and If a coplanar subset includes more than two gyroscopic actuators, the iterative implementation of: o the determination of a residual angular momentum to be provided by the gyroscopic actuators of the sub-assembly, excluding the reference gyroscopic actuator, and o the determination of the direction of an angular momentum of an additional reference gyroscopic actuator from an additional angular separation parameter between the angular momentum to be provided by the additional reference gyroscopic actuator and the direction of the residual angular momentum.

[0019] According to another object, a method for controlling a set of gyroscopic actuators of a satellite is described, each gyroscopic actuator comprising a flywheel capable of being driven in rotation about an axis of rotation so as to produce an angular momentum, and a device for tilting the axis of rotation according to an angle of inclination o, the gyroscopic actuators being distributed into two coplanar subsets, one of the subsets comprising a gyroscopic actuator configured to generate angular momentum contained in a first plane, and the other subset comprising at least two gyroscopic actuators configured to generate respective angular momentum contained in the same second plane of the subset, the first and second planes being non-coplanar, the method comprising: the reception of a dimensionless setpoint angular momentum to be generated by all gyroscopic actuators, The determination of an angular momentum to be provided by each coplanar subset, from the setpoint angular momentum, and a distribution parameter, chosen according to a predetermined sequence of distribution parameters between the two coplanar subsets of gyroscopic actuators, of a component of the setpoint angular momentum (along an axis common to the two planes, in which the parameter r is a scalar chosen between a minimum value and a maximum value corresponding respectively to the lowest permissible value and the highest permissible value of the contribution of one of the coplanar subsets to the setpoint angular momentum along the axis common to the two planes, and the determination of a tilt angle value for each gyroscopic actuator of a coplanar subassembly, based on the determined angular momentum to be provided by said coplanar subassembly, and the emission of a command from each gyroscopic actuator including the respective determined tilt angle value.

[0020] According to another object, a computer program product is described, comprising code instructions for implementing one of the processes according to the preceding description, when executed by a computer.

[0021] According to another object, a computer is described, configured for the implementation of one of the processes according to the preceding description, for the attitude control of a satellite.

[0022] According to another object, a satellite is described, comprising: a set of gyroscopic actuators, each gyroscopic actuator comprising a flywheel capable of being driven in rotation about an axis of rotation so as to produce an angular momentum, and a device for orienting the axis of rotation according to an angle o, the gyroscopic actuators being distributed in two coplanar subsets, each coplanar subset comprising at least two gyroscopic actuators configured to generate an angular momentum hi contained in the same respective plane of the subset, the respective planes of the two subsets being non-coplanar, and a satellite control device, adapted to implement one of the control methods according to the preceding description.

[0023] The proposed control method allows for the determination, for a given angular momentum to be provided by a gyroscopic actuator array formed of two coplanar sub-assemblies, of a position, i.e., an angle, of each gyroscopic actuator. This determination is made according to a specific method, notably based on a distribution parameter, between the two sub-assemblies, of a component along an axis common to the planes of the two sub-assemblies, of the angular momentum to be provided by the array. The control of the gyroscopic actuators, based on a given value of the setpoint angular momentum, is developed according to the precise method and deterministic is advantageously reproducible in ground simulation and allows to know exactly the state of the cluster of gyroscopic actuators.

[0024] Furthermore, determining a value for the distribution parameter associated with the distribution method allows for the precise delimitation of areas to be avoided, corresponding to singular or low-controllability angular momentum zones of the array. Therefore, the distribution parameter in the distribution method according to the invention can be determined as needed to correspond to angular momentum values ​​outside the exclusion zones. Thus, depending on the mission requirements, it is possible to determine a distribution parameter value for the method according to the invention that allows singular areas to be positioned outside the angular momentum values ​​required for mission execution, thereby increasing the satellite's operational capabilities. Brief description of the drawings

[0025] Other features, details, and advantages will become apparent upon reading the detailed description below and analyzing the attached drawings, on which: Fig. 1

[0026] [Fig. 1] represents a schematic diagram of a gyroscopic actuator. Fig. 2

[0027] [Fig. 2] schematically represents the arrangement of an example of a set of gyroscopic actuators. Fig. 3a

[0028] [Fig. 3a] represents an example of angular momentum capability domain of a set of gyroscopic actuators comprising a subset of three coplanar gyroscopic actuators and a subset of two coplanar gyroscopic actuators. Fig. 3b

[0029] [Fig. 3b] represents an example of angular momentum capability domain of a set of gyroscopic actuators comprising two subsets of two coplanar gyroscopic actuators. Fig. 4

[0030] [Fig. 4] is a graphical representation of the parameter r of the distribution of the contribution, to the x component of the angular momentum to be provided by the set of gyroscopic actuators, by one of the two subsets of actuators. Fig. 5

[0031] [Fig.5] represents the angles of two coplanar actuators of a subset determined from the component of angular momentum in the plane of the subset. Fig. 6a

[0032] [Fig. 6a] represents an example of the set of singular configurations of a 2x 2 CMG cluster for a first value of the distribution parameter r. Fig. 6b

[0033] [Fig. 6b] represents another example of the set of singular configurations of a 2 x 2 CMG cluster for another value of the distribution parameter r. Fig. 7a

[0034] [Fig. 7a] represents an example of the angular momenta of a subset of three coplanar gyroscopic actuators to obtain a first value of a component of a setpoint angular momenta in the plane of the actuators. Fig. 7b

[0035] [Fig. 7b] represents an example of the angular momenta of a subset of three coplanar gyroscopic actuators to obtain a second value of a component of a setpoint angular momenta in the plane of the actuators. Fig. 8a

[0036] [Fig. 8a] schematically represents the main steps of a process according to one embodiment. Fig. 8b

[0037] [Fig. 8b] schematically represents the main steps of a process according to another embodiment. Fig. 9

[0038] [Fig. 9] schematically represents a satellite in orbit around the Earth, for which the method of controlling gyroscopic actuators can be implemented. Detailed description of at least one embodiment

[0039] In the present, the terms "gyroscopic actuator" or "CMG" may be used interchangeably to refer to a gyroscopic actuator.

[0040] The set G of gyroscopic actuators distributed into two subsets described below may be referred to as a "cluster" of gyroscopic actuators.

[0041] The notation Ny + Nz CMG will be used to denote the configuration of a gyroscopic actuator array, where Ny and Nz respectively represent the number of gyroscopic actuators in each of the two coplanar subsets. Alternatively, the notation "2 x 2 CMG" can be used, which corresponds to the "2 + 2 CMG" configuration.

[0042] With reference to Figure 2, a schematic example of the configuration of a set G of gyroscopic actuators 10 of a satellite is shown. As described previously in Referring to Figure 1, each gyroscopic actuator 10, or CMG, comprises a flywheel 11 capable of being driven in rotation about an axis of rotation, so as to produce a constant angular momentum of magnitude h, and a device for orienting the axis of rotation of the flywheel by an angle α. The angle α therefore also corresponds to the orientation of the angular momentum produced by the gyroscopic actuator. In Figure 2, each arrow in a plane Pxy and Pxz schematically represents the angle of the axis of rotation of the flywheel of a gyroscopic actuator, i.e., the direction of the actuator's angular momentum. For the purposes of this disclosure, all the gyroscopic actuators 10 in the assembly are assumed to be identical, and therefore have the same angular momentum h.

[0043] As schematically represented in Figure 2, the set G of gyroscopic actuators 10 is divided into two coplanar subsets. In a coplanar subset, the gyroscopic actuators of the same subset are configured so that the angular momentum of each gyroscopic actuator can be oriented in the same plane, i.e., with respect to the same axis that is orthogonal to that plane. Although the two planes corresponding to the two coplanar subsets can be orthogonal, this is not a limiting case. However, the two planes of the two subsets are not parallel.

[0044] Each coplanar subset can include between two and four gyroscopic actuators, for example, two or three gyroscopic actuators. However, the number of gyroscopic actuators is not necessarily the same for both subsets. This disclosure therefore applies, for example, to the cases 2 x 2 CMG, 2 + 3 CMG, 3 + 3 CMG, etc. Furthermore, this disclosure also applies to a special case described in more detail below, denoted 1 + 2 CMG, in which one subset includes at least two coplanar gyroscopic actuators, and the other subset includes only one gyroscopic actuator. This case may correspond, in particular, to a failure of one gyroscopic actuator in one of the two subsets of an initial 2 x 2 CMG configuration.

[0045] Returning to Figure 2, it represents the example of a configuration with four gyroscopic actuators 10 distributed into two subsets of two gyroscopic actuators each, and arranged in two distinct non-coplanar planes.

[0046] By convention, a direct normalized frame of reference R is defined. g linked to all gyroscopic actuators and formed by the three unit vectors (X g , Y g , Z g ) defined as follows: The line forming the intersection of the two planes carries the unit vector X g , The unit vector Y g is orthogonal to X g within the first plane, called PXY, the unit vector Zg is orthogonal to X_ g within the second plane, named PYZ.

[0047] The orientation of the vectors is defined such that the coordinate system g = (X_g, Y g , Z g') either direct. This frame of reference is not necessarily orthogonal; it is only so if the angle between the two planes is equal to 90 degrees.

[0048] In each plane, we denote by 0 the angle formed by the axis of rotation of a gyroscopic actuator i of a subset with respect to a common origin for all gyroscopic actuators defined by the vector Xg. By convention, the sign is positive towards the direction vector of each plane (Y_ g for PXY, Z g for Pxz). In the example shown in Figure 3, the angles ( <r1; <r2; ct3; ct4) des quatre actionneurs gyroscopiques avec <r1>0; <r2< 0; <r3< 0; ct4< 0.

[0049] With these assumptions and notations, the angular momentum h grappe generated by the G cluster of gyroscopic actuators is expressed as follows, as a function of the angles: Eq.1: h grappe = H x X g + H y Yg + H z Z g with Where we have noted in this equation ie P XY the set of gyroscopic actuators i belonging to the coplanar subset of plane P XY and ie P xz the set of gyroscopic actuators i belonging to the coplanar subset of plane P xz .

[0050] We define the dimensionless angular momentum = (x;y;z) = h grappe / h as the ratio between the physical angular momentum generated by the cluster h grappe = ( H x ; H y ; H z ) [Nms] and the individual angular momentum of the CMG h. It is assumed that the gyroscopic actuators are free to rotate and are therefore not subject to any physical or software constraints, so that <r = («T...; ct n ) can reach any value of the space, where N corresponds to the number of gyroscopic actuators in the set. By handling the modulo 2n we can restrict this gimbal angular space to ]-7r,7r] N for example, or equivalently to [0.2TT[ N , without loss of generality.

[0051] The dimensionless angular momentum generated by the cluster is obtained as the image of<r par une fonction non-linéaire H vers un sous-ensemble T> of IR 3 defined as follows: X => COS < 7 H; [0, 2n[ N — > D c IR 3 y = sin rr, Eq.2 A a → A = ( (x; y; z) iePxY z = sin <7, ' 6P xz

[0052] The space D containing all the realizable angular momenta of the cluster G is called the angular momentum capacity domain (dimensionless). A necessary and sufficient condition for the existence of a solution is written: E q.3: 3 x PxY ; x Pxz |x PxY + x Pxz = x; X PXY2 + y 2 < N y 2 x p xz 2 + z 2 < N z 2 Where x PxY is the contribution to x of the subset of coplanar gyroscopic actuators of the plane P XY , etx Pxz is the contribution to x of the subset of coplanar gyroscopic actuators of the plane P xz , N y is the number of gyroscopic actuators in the coplanar subset of plane P XY and N z is the number of gyroscopic actuators in the coplanar subset of plane P xz From this, we deduce the domain D of dimensionless angular momentum (x; y; z) realizable by the cluster, defined by the following system of three inequalities: Eq. 4: "D = x,y, z E IB 3 | |y| < N y ; |z| < N z ; |x| < — y 2 + JN Z 2 — z 2 j

[0053] Referring to Figures 3a and 3b, the angular momentum domain T> is represented by a cluster formed respectively of 2 + 3 CMGs and 2 x 2 CMGs. That is, for Figure 3a, a cluster in which one subset comprises two gyroscopic actuators and the other three gyroscopic actuators, and for Figure 3b, a cluster of two subsets of two gyroscopic actuators. In both cases, terminal disks are observed at + / - Z and + / - Y, the radius of which varies according to the number of gyroscopic actuators in the subset considered.

[0054] Returning to equation 2, this equation describes the relationship = between the angles of the gyroscopic actuators and the (dimensional) angular momentum generated by the array. This system can be explicitly inverted, allowing the determination of all solutions enabling the realization of a given dimensionless angular momentum (x; y; z), subject to feasibility due to the maximum angular momentum capacity of the array (i.e., e D must be greater than or equal to e). This system includes one degree of freedom related to the distribution of angular momentum between the two planes.

[0055] Considering the angular momentum to be provided by the gyroscopic actuator array, this angular momentum is divided into two components ft PxY and ft Pxz respectively in the two planes P XY and P xz Thus, we have: ■h = ftPxy + ftPxZ

[0056] We therefore introduce a distribution parameter r, between the two coplanar subsets, of the component of the angular momentum along the direction common to the two subsets, that is to say the component x along the axis X_g according to the preceding notations.

[0057] The parameter r is defined as follows: (

[0058] Where x ^? represents the lowest possible contribution of the gyroscopic actuators of the coplanar subset corresponding to plane P XY to the x component along the X_g axis of the total angular momentum to be generated by the assembly, and x^ x is the highest possible contribution.

[0059] According to the notations above, h PxY = PXY + y h Pxz = x Pxz + z

[0060] These minimum and maximum contributions of the CMG contribution of plan P XY the x component are given by the following equation: jj ^ ( i - | l ■ x + A MI Zz" 4 "Z 2 ') I and 0 < r < 1

[0061] The distribution parameter r is, for example, a scalar between 0 and 1, which can be seen as a distribution slider for the x component of the total angular momentum provided by the gyroscopic actuators: The value r = 0 positions the contribution of the gyroscopic actuators of the P plane xy to the component x at its lowest admissible value x^, and therefore that of the plane P xz at its maximum value, The value r=1 positions the contribution of the gyroscopic actuators of the P plane XY to the component x at its highest admissible value x^ x and therefore that of the plan P xz at its minimum value, A choice r = 0.5 positions the contributions of the two subsets of the P planes XY and P xz in the middle of the permissible distribution range.

[0062] Referring to Figure 4, the meaning of the distribution parameter r is graphically represented in the case of a 2 x 2 CMG example. In this case, solving the problem of realizing a given dimensionless angular momentum using the set of gyroscopic actuators requires that the distribution solutions in (x) p xv; X PXZ ) comply with the following constraints derived from equation 4 introduced above, applied to the 2 x 2 CMG case: X P XY + x Pxz = x with |x PxY | < J 4 — y 2 and |x Pxz | < Y / 4 — z 2

[0063] Graphically, these conditions are represented as illustrated in Figure 4. The segment between x^ n and x^ x represents the range of values ​​of the distribution parameter r.

[0064] The choice of the parameter ra impacts the location of the angular momentum singularities that can be generated by the set of gyroscopic actuators. The torque generated by the set of gyroscopic actuators around a given position is expressed by differentiating the angular momentum as follows: Cg = -h À with À = (x;ÿ;z)

[0065] This equation can be reformulated as a matrix equation showing the local Jacobian of the linear function H:<r -> , dependent on the angles of the gyroscopic actuators, <7(0: I UJL read J -fi- = 3W ô — with J(CT) = — - - \ oc

[0066] In the case, for example, of a set of 2 x 2 gyroscopic actuators, the Jacobian is of dimension 3 x 4, and defined as follows: — sin <r ± — sin <r2— sin < T3— sin cr4 W(CT)\ <7(0 = cos <r1cos 0 0 do) 0 0 COS CF 3 COS ff4

[0067] The Jacobian depends on the state of the angles of the gyroscopic actuators and is therefore not constant. A particular situation arises if, for a certain state of the cluster defined by the position ct s The torques generated, regardless of the speed command, are always orthogonal to a certain direction U. We then say that the configuration ct s The cluster is singular, and the direction U x which is non-commandable is called singular direction for this configuration.

[0068] The singularity of a configuration of angles of the gyroscopic actuators ct s is equivalent to the existence of at least one zero singular value in the local Jacobian matrix which in turn is equivalent to the fact that the determinant of the matrix JCCT J^CT.;) is zero.

[0069] Since the determinant is a continuous function, and the Jacobian is also continuous in ct, this determinant constitutes an interesting and practical metric of the "distance to singularity" for a given configuration in cardan space.

[0070] The controllability index O for a cluster state ct is defined as follows: 0(0 d =' det(j(CT)J f (CT) In summary, a cluster configuration <r s for which O = ° is singular. In such a case, it is not possible to locally achieve any instantaneous torque control with finite cardan speeds; there is at least one direction of the controlled torque that is not physically realizable.

[0071] However, the value of the distribution parameter ra plays a significant role in the localization of singular configurations. Referring to Figures 6a and 6b, two examples of areas of reduced controllability, corresponding to the singular configurations of the assembly, are shown in the angular momentum capability domain for a gyroscopic actuator array composed of 2x2 CMGs, for two different values ​​of this parameter. Figure 6a represents the case r = 0.5, where the singularities are located in the center of the angular momentum capability domain, and Figure 6b represents the case r = 0.75, where the singularities are located further to the periphery of this domain. Depending on the nature of the mission planned for the satellite, and the requirements By considering the factors associated with the satellite's attitude control, a more appropriate value for r can be selected. If necessary, a temporal sequence of different successive values ​​of r can also be planned during the mission.

[0072] With the parameter r defined, the system (Eq. 2) can be reformulated as follows, showing the distribution of the x component between the two planes: y cos ct, = x PxY ieP XY with x PxY + x Pxz = x ) ' sin ffj = y ieP XY

[0073] In this "separate" form, the system can be solved. We will now present how the system is solved based on the configurations of all the gyroscopic actuators. Case of the 2x 2 CMG configuration

[0074] In the case of the 2 x 2 CMG configuration, and using the notations from Figure 2 for the indices of the gyroscopic actuators, equation 5 can be reformulated as follows: cos a1 + cos a2 = * PxY COS ff3 + COS ff4 = X Pxz Eq. 8 with x PxY + x Pxz = x sin a1 + sin a2 = y sin <r3+ sin <r4= z

[0075] And we obtain these solutions in terms of angles from the gyroscopic actuators. <r = <r1;<r2;<r3;<r4) comme suit en fonction de la commande = (x;y;z) de moment cinétique de grappe et de la répartition choisie (x PxY ;x Pxz ), ff i,2 = A Arg r(xP F x x v Y + j-yA) ± acos - l PxY -+ -yyl with x PxY + x Pxz = x |x Pxz + jz\ °3.4 = Arg(x xz + yz) + acos - - -

[0076] According to (Eq. 9), if we place ourselves in one of the two planes, for example PXY without restriction of generality, the realization of a dimensionless angular momentum control (x xr ; y) is achieved by positioning the rotation axes of the gyroscopic actuators according to the following angles: fa = Arg(x PxY + yy) Eq. 10 <r l 2 = a + ô with | P XY + j y \ I 8 = acos - 2

[0077] Figure 5 graphically represents the components a (median angle of the two gyroscopic actuators of the subset) and 8 (half-differential angle between the two gyroscopic actuators of the subset).

[0078] We can introduce a parameter y here 2CMG e {-1 ; 1} which corresponds to the sign of the angular displacement of a reference gyroscopic actuator, index 1, with respect to the direction of the angular momentum to be generated by the coplanar sub-assembly h p ^-. r CT1 = a + Y 2CMG -S eq U2 = a - y 2CMG .5

[0079] Once the parameter y 2CMG Once fixed, the position of the second gyroscopic actuator is completely determined. In the case where ||ft p(an || = 0, 8 = 90 deg and a can take any value.

[0080] Thus, the angles of the gyroscopic actuators of a coplanar subset of two actuators can be determined. This is true for the 2 x 2 CMG configuration but also for all 2 + N CMG configurations comprising a subset of two gyroscopic actuators. Case of N configurations v + N z CMG where N v and / or N z is greater than 2

[0081] In the case where at least one coplanar subset of gyroscopic actuators comprises three or more actuators (the example from the following plan P is always taken). XY (without loss of generality), there exists one (or more) additional degree(s) of freedom for distributing the angular momentum component generated by the subset. Figures 7a and 7b show two examples of angular momentum to be generated by a coplanar subset of three gyroscopic actuators, with several possible angles Oi for the gyroscopic actuators to achieve these angular momenta. Depending on the value of Ny, the number of additional degrees of freedom can exceed one. Beyond two, each additional CMG provides one additional degree of freedom for generating angular momentum in the planar subset.

[0082] To characterize the additional degree of freedom in the 3 CMG plane, we propose to consider a reference gyroscopic actuator CMGref, as well as the angular separation between the angular momentum to be provided by the reference gyroscopic actuator and the angular momentum to be provided by the coplanar subset. The maximum value 8 max This angular separation occurs when the two other gyroscopic actuators are aligned and is equal to ||ft PxY || < 3: pmax = aCOs(|(j|ft PxY || - || ft P XY ||)^ si he ftPXY ll > 1 K $max = 77 Otherwise

[0083] In what follows, we consider the gyroscopic actuator with index 1 as the reference actuator. We introduce the parameter y 3CMG e [-1, 1] which parameterizes the angular deviation between the angular momentum of the reference CMG with respect to the direction of the angular momentum to be provided by the coplanar subset ft PxY o', = a + Y 3CMG -8 max

[0084] Once y has been determined or fixed 3CMG There remains one degree of freedom corresponding to the two possible permutations of the remaining CMGs. It then suffices to apply the method described above to a subset of two coplanar actuators once the contribution of the reference gyroscopic actuator, i.e., h, has been removed. res = [ / L.1 = h plan - [ C ° S ^ CT| ?]. L h£ es J Lsinfajj _ ^res i -,2CMG rres o2- a + yd -,2CMG vres U g — LC y ■ U With: fa res = atan2 h y res ,h x res ) eq, 12' ||ftr eS || (5 res = acos(2)

[0085] In the case of a coplanar subset comprising more than three gyroscopic actuators, this approach can be implemented iteratively as follows: We determine the parameter y NCMG e [-1, 1] which parameterizes the angle of the angular deviation between the direction of the angular momentum of a first reference gyroscopic actuator with respect to the direction of the angular momentum to be provided by the coplanar subset ft PxY We consider the remaining angular momentum h res once we have removed the contribution of the reference CMG, that is to say h res = [, 1 = ft p xy > c ° s ^ CTref ^l, J Lsin (ff ref )J We determine the parameter y^ -1 CMG e [-1, 1] which parameterizes the angle of the angular deviation between the first remaining CMG, considered as a second reference gyroscopic actuator, with respect to the direction of the remaining angular momentum h res , The remaining angular momentum is considered after removing the contribution of the second reference CMG, iterating these steps until only two gyroscopic actuators remain between which the remaining angular momentum can be distributed. The angles of these two gyroscopic actuators are then determined, and then, taking into account the values ​​of the parameters y N ~ 1 CMG , yNCMG q U j on Once the reference CMGs have been fixed, we can determine their contributions. Case of configuration N v = 1 and N z > 2 CMG

[0086] As previously mentioned, the case where one of the coplanar subsets comprises only a single gyroscopic actuator can represent a failure. In this case, the necessary and sufficient condition for the existence of a solution is written, under the non-limiting assumption that the coplanar subset reduced to a single CMG corresponds to the PXY plane: 3 x PxY ; x Pxz | x PxY + x Pxz = x; x Pxy2 + y 2 = 1; x Pxz2 + z 2 < N z 2

[0087] The difference from the previous cases stems from the fact that the amplitude of the angular momentum in the PXY plane of the gyroscopic actuator alone cannot be modulated. Thus, the inequality concerning the The capacity in the PXY plane is transformed into an equality. Solving this equation yields two solutions: 1 -y 2

[0088] In the case of a single gyroscopic actuator in one of the planes (in this case PXY), the contribution of the gyroscopic actuator in plane PXY to the x component of the total angular momentum generated by the array therefore only has two solutions. Thus, the distribution parameter r can only take two possible values: 0 or 1. f X m7n = -Vl -y 2 1 X max = 'J' i - - y 2 Y and r = 0, our = 1

[0089] In light of the foregoing, and with reference to Figures 8a and 8b, the principles set forth above are used in a method for controlling a set G of gyroscopic actuators 10 of a satellite S, to cause these gyroscopic actuators to generate a set angular momentum and thus enable attitude control of the satellite. The satellite S is equipped with such a set of gyroscopic actuators 10 distributed into two subsets, where, if a subset comprises at least two gyroscopic actuators 10, the subset is coplanar, and with a control device 20 for said actuators, schematically represented in Figure 9.

[0090] The satellite in which this process is implemented can, for example, be an Earth observation satellite, carrying at least one observation instrument. The satellite can be intended to be operated in low Earth orbit (LEO), medium Earth orbit (MEO), or geostationary orbit (GEO).

[0091] In some embodiments, the satellite mission is predetermined, such that a target attitude (which may vary over time) for the satellite is determined a priori for the entire mission duration, and the torque requirements generated by all the gyroscopic actuators to maintain or change the satellite's attitude are also known. Based on these requirements, at least one value, or a time sequence of values, of the target angular momentum is determined.

[0092] Furthermore, one or more values ​​of the distribution parameter r introduced above is / are predetermined. The sequence of values ​​can, for example, represent a curve of successive discrete values, or successive levels, or be constant. The sequence can be continuous or discontinuous.

[0093] The value sequence can be determined, in particular, according to the mission requirements and the arrangement of singularity zones (or areas of reduced controllability) related to the choice of parameter r. In some embodiments, the value of parameter r can be constant for the entire duration of the mission. Alternatively, parameter r can exhibit a value profile that varies over time during the mission. Alternatively, the torque requirements to be generated by The set of gyroscopic actuators can be determined during the mission and, depending on these needs, one or more values ​​of the distribution parameter r can be determined.

[0094] Depending on the configuration of the gyroscopic actuator set, one or more parameters y, equal to -1 or 1, are also determined, fixing the angular separation between a reference gyroscopic actuator and the direction of the angular momentum to be generated by a coplanar subset. This is as described above regarding the parameters y 2 ™ 6 ^ 3 ™ 6 , etc., the number of parameters y depends on the number of gyroscopic actuators in the subset, and more specifically there is an N-1 number of parameters y fixed for a subset of N gyroscopic actuators.

[0095] The process includes a step 100 of receiving a setpoint angular momentum ^cluster > (pj*. pj?. provided by the set G of gyroscopic actuators 10, that is to say that this setpoint angular momentum must be realized jointly by the set of gyroscopic actuators. This setpoint angular momentum can be reduced to the dimensionless angular momentum = (x;y;z) = h 9rappe / h introduced above. The setpoint angular momentum may, for example, have been determined from an instantaneous torque to be supplied by the gyroscopic actuators.

[0096] The process then includes, from the received setpoint angular momentum, the implementation of an inversion 200 of this setpoint angular momentum to determine the angles o of the set of gyroscopic actuators 10 allowing to generate this setpoint angular momentum, and the sending 300 of a setpoint to the gyroscopic actuators with an indication of the angle to adopt.

[0097] In some embodiments, steps 100 and 200, which determine the angle values ​​of the gyroscopic actuators, are carried out by a ground station T, which then communicates the gyroscopic actuator angle values ​​to be used to the satellite S. The ground station may, for example, include at least one processor and at least one electronic memory (not shown) in which a computer program product is stored, in the form of code instructions to be executed to implement steps 100 and 200 of the process. In another variant, the ground station includes one or more programmable logic circuits, such as FPGAs, PLDs, etc., and / or specialized integrated circuits (ASICs) adapted to implement these steps.

[0098] Alternatively, steps 100 and 200, as well as step 300 of sending a command to the gyroscopic actuators, are implemented by the control device 20 on board the satellite, which may also include at least one or more processors (CPU, DSP, GPU, FPGA, ASIC, etc.) and a memory (magnetic hard drive, electronic memory, optical disk, etc.) in which are stored the code instructions executed by the processor, as well as the values ​​of the parameters determined for the implementation of the mission.

[0099] The inversion step 200 includes determining the angle Oi of each gyroscopic actuator, from the setpoint angular momentum and the distribution parameter r. The parameter r allows us to determine the contribution x. PxY , x p xz of each coplanar subset to the x component of the angular momentum along the axis common to the two planes, by application of equation 5 above, where the minimum and maximum permissible contributions of the subset are determined as a function of the number of gyroscopic actuators and the setpoint angular momentum by equation 6.

[0100] Consequently, the angles of the gyroscopic actuators of each sub-assembly are determined from the angular momentum to be provided by each sub-assembly, i.e., x PxY + y for the subset corresponding to the plane P XY , and x Pxz + z, for the subset corresponding to the plane P xz .

[0101] In some embodiments, this determination 220 of an angle value of each gyroscopic actuator from the angular momentum to be provided by each subassembly comprises: The determination 221 of an angle of at least one reference gyroscopic actuator, from the angular momentum to be provided by the subassembly and at least one parameter y defining an angular separation between the angular momentum to be provided by this reference gyroscopic actuator and the angular momentum of the subassembly, and The determination 223 of an angle value of each other gyroscopic actuator of the subset from the angle of the reference gyroscopic actuator.

[0102] With reference to Figure 8a, in cases where the satellite includes at least one subset of two coplanar gyroscopic actuators, the determination of the angle in of each actuator of this subset is carried out by application of Equation 11 introduced above, where the reference gyroscopic actuator has an angle a.

[0103] With reference to Figure 8b, when the satellite includes at least one subset of three or more gyroscopic actuators, the determination 220 of the angle in of each actuator in that subset includes: The determination 221 of an angle of a first reference gyroscopic actuator, from the angular momentum to be provided by the subassembly ft PxY and at least one parameter ^CMG defining an angular separation between the angular momentum to be provided by this reference gyroscopic actuator and the angular momentum of the sub-assembly, The iterative implementation, until the number of gyroscopic actuators excluding the reference gyroscopic actuator(s) reaches two, of the following steps: • determination 222 of a residual angular momentum h res to be provided by the gyroscopic actuators of the subassembly, excluding the reference gyroscopic actuator(s), • determination (221) of the direction of an angular momentum of an additional reference gyroscopic actuator from parameters y N ~ 1CMG defining the sign of an angular separation between the angular momentum to be provided by the additional reference gyro actuator and the direction of the residual angular momentum. We thus iteratively reduce to a case of two residual gyroscopic actuators, where it is possible to determine the angles of these actuators during a step 223 as in the case described above with reference to Figure 2a. The angles of the reference gyroscopic actuators are then deduced from the values ​​of the y parameters.

Claims

Demands [Claim 1] Method for controlling an assembly (G) of gyroscopic actuators (10) of a satellite (S), for the realization by the gyroscopic actuators of a setpoint angular momentum, each gyroscopic actuator (10) comprising a flywheel (11) capable of being driven in rotation about an axis of rotation so as to produce an angular momentum, and an orientation device (12) of the axis of rotation at an angle o, the gyroscopic actuators being distributed into two coplanar subsets, each coplanar subset comprising at least two gyroscopic actuators configured to generate a respective angular momentum contained in the same plane of the subset, the respective planes of the two subsets being non-coplanar, the ordering process including: The reception (100) of a dimensionless setpoint angular momentum ( (x;y;z)) to be generated by all the gyroscopic actuators, The determination (210) of an angular momentum to be provided by each coplanar subset (ft PxY , ft Pxz ), starting from the dimensionless setpoint angular momentum and a distribution parameter (r) chosen according to a predetermined sequence of distribution parameters, between the two coplanar subsets, a component (x) of the setpoint angular momentum is distributed along an axis (X5) common to the two planes, where the parameter r is a scalar between a minimum value and a maximum value corresponding respectively to the lowest permissible value (x^) and the highest permissible value (x' ')J x) of the contribution of one of the coplanar subsets to the component (x) of the setpoint angular momentum along the axis common to the two planes, The determination (220) of a tilt angle value (ai) of each gyroscopic actuator of a coplanar subset, from the angular momentum (ft PxY , ft PxY ), to be provided by said coplanar subset, and The emission (300) of a command from each gyroscopic actuator including the respective tilt angle value determined (o). [Claim 2] A method according to claim 1, wherein the distribution parameter (r) has at least one predetermined value depending on the mission of the satellite. [Claim 3] A method according to any one of claims 1 or 2, wherein the predetermined distribution parameter (r) exhibits a time-varying value profile during a satellite mission. [Claim 4] A method according to any one of the preceding claims, wherein the parameter r is defined as follows: where x PxY and x p xz are respectively the angular momenta generated, along the common axis ( ff ) to the two planes, by the two coplanar subsets, x^ n is the lowest permissible value of the contribution of a subset to said component of the setpoint angular momentum along the common axis ( ff ) to both planes, x^ x is the highest permissible value of the subset's contribution to the (x) component of the setpoint angular momentum along the axis ( s common to both plans. [Claim 5] A method according to the preceding claim, wherein - - is defined as H; [0, 2n[ N D c B 3 sin ct, Eq.2 ct —> A = (x; y; z) ieP XY sin ct, and in which we define x^X and xJ^L as (JJ) Eq.6: ■ x^L = min ( i -| N v 2 - y 2 ; x + Al N z 2 - z 2 And [Claim 6] A method according to any one of the preceding claims, wherein the determination (220) of an angle value of each gyroscopic actuator of a coplanar subassembly from the angular momentum to be provided by said subassembly comprises: The determination of a direction of angular momentum (hi) to be provided by each gyroscopic actuator, from the angular momentum to be provided by the subset (hPxy, hPxz), and at least one predetermined parameter (y), defining an angular separation between the angular momentum to be provided by a reference gyroscopic actuator and the angular momentum to be provided by the subset, and Determining the tilt angle value of each gyroscopic actuator from the corresponding angular momentum direction. [Claim 7] A method according to claim 5, wherein the step of determining a direction of angular momentum to be performed by each gyroscopic actuator comprises: the determination of the direction of the angular momentum of a reference gyroscopic actuator from a first angular separation parameter and the direction of the angular momentum to be provided by the subassembly, and If a coplanar subset includes more than two gyroscopic actuators, the iterative implementation of: o the determination of a residual angular momentum to be provided by the gyroscopic actuators of the sub-assembly, excluding the reference gyroscopic actuator, and o the determination of the direction of an angular momentum of an additional reference gyroscopic actuator from an additional angular separation parameter between the angular momentum to be provided by the additional reference gyroscopic actuator and the direction of the residual angular momentum. [Claim 8] Method for controlling a set of gyroscopic actuators of a satellite, each gyroscopic actuator comprising a flywheel capable of being driven in rotation about an axis of rotation so as to produce angular momentum, and a device for tilting the axis of rotation according to an angle of inclination o, the gyroscopic actuators being distributed into two coplanar subsets, one of the subsets comprising a gyroscopic actuator configured to generate angular momentum contained in a first plane, and the other subset comprising at least two gyroscopic actuators configured to generate respective angular momentum contained in the same second plane of the subset, the first and second planes being non-coplanar, the method comprising: The reception (100) of a dimensionless setpoint angular momentum h(x,y,z) to be generated by all the gyroscopic actuators, The determination (210) of an angular momentum to be provided by each coplanar subset (ft PxY , ft Pxz), from the setpoint angular momentum, and a distribution parameter (r), chosen according to a predetermined sequence of distribution parameters between the two coplanar subsets of gyroscopic actuators, of a component of the setpoint angular momentum (hx) along an axis common to the two planes, in which the parameter r is a scalar chosen between a minimum value and a maximum value corresponding respectively to the lowest permissible value and the highest permissible value of the contribution of one of the coplanar subsets to the setpoint angular momentum along the axis common to the two planes, and The determination (220) of a tilt angle value (o) of each gyroscopic actuator of a coplanar subset, from the determined angular momentum (ft PxY , ft Pxz ), to be provided by said coplanar subset, and The emission (400) of a command from each gyroscopic actuator including the respective tilt angle value determined (o). [Claim 9] Product computer program, comprising code instructions for implementing the method according to any one of the preceding claims, when executed by a computer. [Claim 10] Computer, configured for the implementation of the method according to any one of claims 1 to 8, for the attitude control of a satellite. [Claim 11] Satellite (S), comprising: an assembly (G) of gyroscopic actuators (10), each gyroscopic actuator (10) comprising a flywheel (11) capable of being driven in rotation about an axis of rotation so as to produce an angular momentum, and a device (12) for orienting the axis of rotation at an angle θ, the gyroscopic actuators (10) being distributed into two coplanar subassemblies, each coplanar subassembly comprising at least two gyroscopic actuators configured to generate an angular momentum hν contained in the same respective plane of the subassembly, the respective planes of the two subassemblies being non-coplanar, and a control device (T, 20) of the satellite, adapted to implement the control method according to any one of claims 1 to 8.

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